Create a system of equation that has no solution:
- write the equations in two different forms(4)
Create a system of equation that has infinitely many solution
- write the equations in two different forms (4)
One important Question:
How am I suppose to form a table out of this with at least 5 points.
no solutions
x+y = 2
x+y = 3
many solutions
x+y = 2
2x+2y = 4
You can rearrange terms to get different forms
For the table, just pick 5 values for x, and calculate the corresponding values for y, using your equation.
So am I suppose to have 2 charts for each
To create a system of equations that has no solution, you can set up two equations that are parallel and will never intersect. Let's use the form y = mx + b to create the equations:
Equation 1: y = 2x + 3
Equation 2: y = 2x - 1
These equations have the same slope of 2 but different y-intercepts. They are parallel lines and will never intersect. Therefore, this system of equations has no solution.
To create a system of equations that has infinitely many solutions, you can set up two equations that represent the same line or two equations that are multiples of each other. Let's use the form y = mx + b to create the equations:
Equation 1: 2x + 4y = 8 => y = -1/2x + 2
Equation 2: 4x + 8y = 16 => y = -1/2x + 2
Both equations are equivalent since they represent the same line - they have the same slope (-1/2) and same y-intercept (2). Any value of x or y will satisfy both equations. Therefore, this system of equations has infinitely many solutions.
To form a table with at least 5 points for any given equation, you can choose values for x and calculate the corresponding y-values using the equation. Here's an example using the equation y = 2x + 3:
Let's choose x values of -2, -1, 0, 1, and 2:
For x = -2: y = 2(-2) + 3 = -1 => Point (-2, -1)
For x = -1: y = 2(-1) + 3 = 1 => Point (-1, 1)
For x = 0: y = 2(0) + 3 = 3 => Point (0, 3)
For x = 1: y = 2(1) + 3 = 5 => Point (1, 5)
For x = 2: y = 2(2) + 3 = 7 => Point (2, 7)
You can continue this process with more values of x to form a table with as many points as you desire.